No because you don't "receive" coins. Sender broadcasts a message (to every single node in the network) that "you" now have control of the coins. What enables you to spend those coins in the future is the fact that you have the private key for the public address coins were sent to.

You (either directly as a full node or indirectly as a lite client/webservice) only need access to the blockchain to verify coins were sent and to spend them.